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arXiv · 2307.04211

Zeros of meromorphic functions of the form $\sum\limits_n \dfrac{c_n}{(z-t_n)^2}$

Anton Baranov·Vladimir Shemyakov
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Abstract

We study zeros distribution for meromorphic functions of the form $\sum\limits_n \dfrac{c_n}{(z-t_n)^2}$, where $\sum\limits_n \dfrac{|c_n|}{|t_n|^2} <\infty$. We prove an analog of the classical Keldysh theorem and discuss a relation between zero-free functions of this form and second order differential equtions with polynomial coefficients.

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Anton Baranov, Vladimir Shemyakov. 2023-07-09. Zeros of meromorphic functions of the form $\sum\limits_n \dfrac{c_n}{(z-t_n)^2}$. https://arxiv.org/abs/2307.04211

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